An instrumental variable (IV) based estimator of a causal effect emerges as the standard approach to mitigate the confounding bias in social science, economics, and epidemiology where randomized experiments can be too costly or even impossible to conduct. However, justifying the validity of the instrument often poses a significant challenge. In this work, we highlight a problem for IV settings that is generally neglected in justificatory arguments of IV validity––the presence of an "aggregate treatment variable", where the treatment (e.g. education, GDP, caloric intake) is made up of finer-grained components that each may have a different effect on the outcome. We first characterize the nature of the causal effect of the aggregate treatment on the outcome and then identify the conditions under which standard IV-based estimators identify the aggregate effect. The results imply major limitations on the interpretation of IV estimates based on aggregate treat-ments and highlight the need for a broader justificatory base of the exclusion restriction in IV settings.
This is joint work with Danielle Tsao, Krikamol Muandet and Ema Perkovic.
